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We propose an axiomatic approach for design and performance analysis of noisylinear consensus networks by introducing a notion of systemic performancemeasure. This class of measures are spectral functions of Laplacian eigenvaluesof the network that are monotone, convex, and orthogonally invariant withrespect to the Laplacian matrix of the network. It is shown that severalexisting gold-standard and widely used performance measures in the literaturebelong to this new class of measures. We build upon this new notion andinvestigate a general form of combinatorial problem of growing a linearconsensus network via minimizing a given systemic performance measure. Twoefficient polynomial-time approximation algorithms are devised to tackle thisnetwork synthesis problem: a linearization-based method and a simple greedyalgorithm based on rank-one updates. Several theoretical fundamental limits onthe best achievable performance for the combinatorial problem is derived thatassist us to evaluate optimality gaps of our proposed algorithms. A detailedcomplexity analysis confirms the effectiveness and viability of our algorithmsto handle large-scale consensus networks.

Growing Linear Consensus Networks Endowed by Spectral Systemic Performance Measures